Product: ABAQUS/Standard
AC1D2 AC1D3
ACAX3 ACAX4 ACAX6 ACAX8
AC2D3 AC2D4 AC2D6 AC2D8
Each member of the family of acoustic elements is used to model an organ pipe. The natural modes of vibration are extracted from the models for the case of an organ pipe with both ends open (open/open) and the case of an organ pipe with one end open and the other end closed (open/closed). The appropriate boundary condition at an open end is that the acoustic pressure degrees of freedom be set to zero (a free surface). A closed end requires no boundary condition; the natural boundary condition is that of a rigid surface adjacent to the fluid. Results are compared with exact solutions.
The model consists of a column of air 165.8 units high with a cross-sectional area of 1.0. The first-order element model consists of 20 acoustic elements along the length of the fluid column and one through the cross-section. The second-order element models consist of 10 elements.
The material properties used for the air are 
= 1.293 and bulk modulus = 1.42176 × 105.
The geometry and material properties defined for this problem result in the natural frequencies of 
= 1.0 cycles/sec, 
= 2.0 cycles/sec, and 
= 3.0 cycles/sec for the open organ pipe and = 0.5 cycles/sec, = 1.5 cycles/sec, and = 2.5 cycles/sec for the closed organ pipe.
The results deviate less than 1% from these frequencies for the first-order elements and less than 0.1% for the second-order elements. More accuracy can be acquired with finer meshes. To match these frequencies with two- and three-dimensional finite elements, the length of the fluid column is chosen considerably longer than the width of the column.
AC1D2 elements.
AC1D3 elements.
ACAX3 elements.
ACAX4 elements.
ACAX6 elements.
ACAX8 elements.
AC2D3 elements.
AC2D4 elements.
AC2D6 elements.
AC2D8 elements.
AC3D4 elements.
AC3D6 elements.
AC3D8 elements.
AC3D10 elements.
AC3D15 elements.
AC3D20 elements.
ACAX3 ACAX4 ACAX6 ACAX8
AC2D3 AC2D4 AC2D6 AC2D8
The models consist of duct-like meshes of length 0.1. The first step consists of an eigenvalue analysis of the model with no boundary conditions. The second step applies a spherical nonreflecting impedance on all exterior ends of the ducts. The third step performs an eigenvalue analysis of the model with the impedance conditions. Results are printed only for the first and third steps.
AC2D3, AC2D4, AC2D6, and AC2D8 elements.
ACAX3, ACAX4, ACAX6, and ACAX8 elements.
AC3D4, AC3D6, AC3D8, AC3D10, AC3D15, and AC3D20 elements.
Acoustic finite elements:
ACAX3 ACAX4 ACAX6 ACAX8
AC2D3 AC2D4 AC2D6 AC2D8
AC3D4 AC3D6 AC3D8 AC3D10 AC3D15 AC3D20
Acoustic infinite elements:
ACINAX2 ACINAX3
ACIN2D2 ACIN2D3
The models consist of duct-like meshes of length 0.1, terminated with acoustic infinite elements. The first analysis step consists of a real eigenvalue analysis of the model. The second step performs a complex eigenvalue analysis of the model.
ACIN2D2, ACIN2D3, AC2D3, AC2D4, AC2D6, and AC2D8 elements.
ACINAX2, ACINAX3, ACAX3, ACAX4, ACAX6, and ACAX8 elements.
ACIN3D3, ACIN3D4, ACIN3D6, ACIN3D8, AC3D4, AC3D6, AC3D8, AC3D10, AC3D15, and AC3D20 elements.